Harmonic mappings in the exterior of the unit disk
Jarosław Widomski; Magdalena Gregorczyk
Annales UMCS, Mathematica (2010)
- Volume: 64, Issue: 1, page 63-73
- ISSN: 2083-7402
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topJarosław Widomski, and Magdalena Gregorczyk. "Harmonic mappings in the exterior of the unit disk." Annales UMCS, Mathematica 64.1 (2010): 63-73. <http://eudml.org/doc/267959>.
@article{JarosławWidomski2010,
abstract = {In this paper we consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition [...] . We are interested in finding radius of univalence and convexity for such class and we find extremal functions. Convolution, convex combination, and explicit quasiconformal extension for this class are also determined.},
author = {Jarosław Widomski, Magdalena Gregorczyk},
journal = {Annales UMCS, Mathematica},
keywords = {Harmonic mapping; meromorphic; quasiconformal extension; radius of convexity; radius of univalence; harmonic function},
language = {eng},
number = {1},
pages = {63-73},
title = {Harmonic mappings in the exterior of the unit disk},
url = {http://eudml.org/doc/267959},
volume = {64},
year = {2010},
}
TY - JOUR
AU - Jarosław Widomski
AU - Magdalena Gregorczyk
TI - Harmonic mappings in the exterior of the unit disk
JO - Annales UMCS, Mathematica
PY - 2010
VL - 64
IS - 1
SP - 63
EP - 73
AB - In this paper we consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition [...] . We are interested in finding radius of univalence and convexity for such class and we find extremal functions. Convolution, convex combination, and explicit quasiconformal extension for this class are also determined.
LA - eng
KW - Harmonic mapping; meromorphic; quasiconformal extension; radius of convexity; radius of univalence; harmonic function
UR - http://eudml.org/doc/267959
ER -
References
top- Hengartner W., Schober G., Univalent harmonic functions, Trans. Amer. Math. Soc. 299 (1987), 1-31.
- Jahangiri, Jay M., Harmonic meromorphic starlike functions, Bull. Korean Math. Soc. 37 (2000), No. 2, 291-301. Zbl0960.30010
- Jahangiri, Jay M., Silverman H., Meromorphic univalent harmonic functions with negative coefficients, Bull. Korean Math. Soc. 36 (1999), No. 4, 763-770. Zbl0955.30011
- Lehto O., Virtanen K. I., Quasiconformal Mappings in the Plane, Springer-Verlag, Berlin-Heidelberg-New York, Second Edition, 1973. Zbl0267.30016
- Pommerenke Ch., Univalent Functions, Vandenhoeck & Ruprecht in Göttingen, 1975.
- Sheil-Small T., Complex Polynomials, Cambridge University Press, 2002.
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